Juve thought they had forced extra time after erasing Madrid's three-goal first-leg advantage by taking a 3-0 lead at the Santiago Bernabeu, until Medhi Benatia was adjudged to have fouled substitute Lucas Vazquez in the final seconds of play - sparking a furious protest from Buffon.
Buffon was seething after the final whistle as he blasted Oliver and his decisions during a passionate post-match interview.
"Right there, you can not ask a man who lives sport as deeply as I do to be balanced, because even if I expressed these feelings in an exaggerated way, they were still logical thoughts".
"If you want to be that protagonist, sit in the ground with your wife".
Buffon who made his 650th appearance for Juve added: "You can not ruin the dreams of a team".
"I think that in a few days, Buffon will have different words to say to the referee". Many have sympathised with Buffon, whereas others have condemned him.
The veteran goalkeeper fumed at Oliver after the decision and was sent off for his aggressive reaction, which saw him scream and point his hand in the English official's face.
The English worldwide praises his countryman for staying cool in the situation, claiming he was "as cool in that moment as Cristiano Ronaldo". I felt defrauded of a night that can never be repeated'.
"I know the referee saw what he saw, but it was certainly a dubious incident".
It's hard to defend Buffon. With regards to Buffon, Gigi has been an example for 20 years of what a man should be both on and off the pitch.
From Manchester United's astonishing victory at the Etihad against their cross-town rivals Manchester City in the Premier League to Roma's historic win against Barcelona at Stadio Olimpico in the Champions League, fans across the globe have witnessed some of the most heart-pounding games in recent times.
For that reason, Buffon must accept the consequences of his actions, but at the same time he also deserves sympathy.